How to make tissue of the mesh
Control orientation with Active UV

Tissue add-on by default takes into account the vertex indices of the face to determine the orientation. If you build your mesh by extruding the same face several times, they should follow the same orientation because the way new faces are generated.

Tissue add-on has an option to override the default orientation given by the vertices indices with the inforamtion of the active UV layout.

If you unwrap your mesh in portions with seams like shown in the image below (notice the different flowing of the color grid texture on the front and on the side):



and then pic the Active UV optin in the Rotation field of the add-on settings, you'll see the tessellated faces following the orientation.



This approach obiuvsly create a discontinuity between the two regions that (if wanted) should be handled manually and other complications if you would like to make the feathers overlap, but the add-on gives a good staring point to work with.